PHYSICS & Related Fields - The SPS Guide to - 2020-2021 Edition - Harvard ...
←
→
Page content transcription
If your browser does not render page correctly, please read the page content below
2020-2021 Edition Table of Contents Introduction 2 The Society of Physics Students 3 Why Should I Study Physics? 4 Ways to Study Physics at Harvard 6 Physics Course Strategies 10 Course Descriptions and Recommendations 13 Freshman Seminars 14 Physics Department Courses 15 Mathematics Department Courses 27 Astronomy Department Courses 33 Other Cool Stuff 34 Research at Harvard 40 Contacts 46 The Back Page 48 1
Introduction The Harvard-Radcliffe Society of Physics Students – SPS for short – has produced this booklet for students who are considering concentrating in physics or a related field. Even if you’re not planning to become a physics concentrator, we hope you’ll find this booklet helpful. It can be hard to decide on a field to concentrate in. It’s also hard to choose which courses to take, whether they’re in the physics department or outside of it. We can’t help you with choosing an Expository Writing class, but we hope our experience as physics concentrators at Harvard will be useful to you. You can use this guide during shopping period, but you might want to keep it in a desk drawer for future reference — it might come in handy over the next few shopping periods. Take the guide out for a walk once in a while, it likes exercise too. Of course, when you’re choosing your concentration and classes, it’s a good idea to get as much information as possible. You can obtain advice from the informational meetings held in the Science Center a few days before classes begin, from individual members of the Physics Department Faculty, from the Head Tutors, and from upper-class students by emailing the SPS list. You can find online resources at www.physics.harvard.edu. In fact, we very strongly encourage you to get advice from as many sources as you can. (Of course, since no one reads the Introduction, we’ll stress this later on too.) Every effort has been made to ensure the accuracy and completeness of the information in this booklet. Nevertheless, it may contain inadvertent errors and omissions, so you should be sure to consult the course information in the my.harvard portal and the student handbook subsection Fields of Concentration before making any final decisions. 2
The Society of Physics Students Our name says it all. The Harvard-Radcliffe Society of Physics Students (SPS) works to promote the interests of physics students at Harvard and Radcliffe. SPS organizes many different kinds of activities throughout the year: academic, career-related, and just-for-fun events. To learn about research going on in the various sub-fields of physics and related areas, be sure to attend the Monday lunches at noon with the visiting colloquium speakers (eat nice food, learn a lot) as well as the Wednesday evening talks with Harvard professors as part of Physics 95 (all are welcome; ice cream served). We also host a number of talks about grad schools and careers for those trained in the physical sciences. Keep your eyes out for events such as movie nights, and liquid nitrogen fun. Don’t miss our annual nitrogen-frozen pumpkin drop on Halloween. Fanciful ideas such as races across non-Newtonian cornstarch have been proposed. The SPS functions as a liaison between the community of physics students and the Physics Department. Periodically, the officers of SPS meet with the chair and undergrad tutors of the department to discuss issues of concern to physics students. We hope all physics students will bring ideas to this process. The physics undergraduate study serves as a great place to relax, meet up with other physics students, and get to know Undergraduate Coordinator (a.k.a. “undergrad mom”) Carol Davis, whose office is across the hall. Look out for sweet snacks and free food! Another important function of the SPS is informing physics students of events that may be of interest to them. SPS has produced this booklet in an effort to ensure that new students are fully informed about the options available to them. There is also an email list, sps-list@hcs (for major SPS and department announcements) as well as a more informal sps-open@hcs (for interesting events, opportunities, class advice, questions from students, and links). If you want to subscribe to the email list, you can visit our website, www.hcs.harvard.edu/~physics. Also, check out our Facebook group (www.facebook.com/groups/168759966574319)! 3
Why Should I Study Physics? Good question. Well, if you ask any physicist this question, they will probably tell you without hesitation: “It’s fun!” Of course, not all of us are destined to become physics faculty. But even if you’re not sure if you want to be a physics pro – in fact, even if you’re not sure you want to be a physics concentrator – we think you should at least take a few physics classes. Give us the chance to convince you. If you want to go into any science, knowledge of physics is a valuable tool to have. Not to toot our own horn too much, but physics is the basis for all phenomena in the understandable universe. Having knowledge of the principles behind all the other sciences leads to a deeper understanding and is a way to avoid silly errors. Do you want to be the biologist or inventor whose ideas violate the conservation of energy? Probably not. A firm grounding in physics can only help your work in other fields. Also, physics is really fun. Even if you’re not sure if you want to go into research at all, knowledge of physics can help you out. As has become more and more clear, the job market of the new millennium is unlike anything we’ve ever seen before. Sociologist Manuel Castells calls it an Information Age, where the thriving center of the economy is based not only on technology but on technology for creating even more technology. Desirable jobs – the kind that pay off Harvard tuition bills – more and more demand rock-solid analytical skills and the ability to understand complex, difficult problems. A physics education is all about that. A physics education is also fun. To put it a little bit more concretely, more and more physics students are taking their undergraduate science degrees into the Big Three areas of professional school: medicine, law, and business. Doctors now routinely perform procedures such as “positron emission tomography” and “magnetic resonance imaging.” The study and development of artificial joints and organs demand cutting edge materials and biophysics knowledge. As debates over cloning and movie pirating have shown us, new sciences and technologies have also led to all sorts of legal and social quandaries. Scientifically educated lawyers who can intelligently wade through these morasses are becoming a valuable commodity. And as business and industry become more ever more technical, the executive who can actually understand their company’s function or product is becoming increasingly valuable. If you’re the Wall Street type, hedge funds and investment banks are always looking for people with the analytical and mathematical skills to do whatever it is they do down there. And they are willing to pay them lots and lots and lots of money. The increasingly important role of technology in our everyday lives has also made clear the need for quality science education in our schools, from 4
elementary to high school. A teacher with a solid science background is a lamentably rare creature, but they are also an immensely valuable resource to a school and to society at large. If you have some physics knowledge under your belt, schools will love you. Also, physics is really fun. Basically, we’ve been saying the same thing in a bunch of ways: physics demands clear logical thinking and strong math skills. Maybe you’re not the kind of person who eats Gaussian integrals for breakfast, but taking even a few physics classes will help you hone your analytical thinking and problem solving. As a bonus, you’ll learn all about the universe that we live in, which it turns out is a lot wackier than it seems at first glance. If you want to learn more about the clever ways physics applies to everyday life, you might think about taking Physics 125. And if you want to know all about the neat stuff going on in the forefront of physics, check out the Physics Department Colloquia (Monday afternoons), or the Wednesday evening lecture series (in conjunction with Physics 95). And pester your professors! In conclusion, you should study physics. It’s fun! 5
Ways to Study Physics at Harvard Harvard is a very exciting place, but it’s a bit confusing for the first few weeks. So much happens before you’ve really figured out where you are! You’ve probably come with a lot of interests, but you may not be sure how to pursue them here. The Society of Physics Students thought we could help you out a little bit as you get acclimated, by giving you some advice on what you can do with your interest in the physical sciences. The first thing to realize is that you have many options. Some choices must be made by November of your sophomore year, when you select a concentration. You could concentrate in physics. You may wish to joint concentrate. You may have the option of advanced standing (in which case these decisions may be upon you even earlier). Or you might take physics classes for a secondary field or as electives, with no thought of concentrating in physics at all. New and different plans of study are constantly being invented, so you should also feel free to dream up just about anything and present it to Howard Georgi (the Head Tutor) or David Morin (the Co-Head Tutor). Chances are they’ve heard worse! (And after all this, you may very likely change your mind about these decisions. No problem—nothing is written in stone!) If you are considering concentrating in physics (or some variation on that theme), this section describes the myriad options for concentration. More details can be found in the Fields of Concentration section of the Student Handbook. Or, you may wish to jump directly to the course descriptions. The Physics Concentration Let’s start with the most straightforward case. You want to concentrate in physics. (Yay!) For non-honors, you must take twelve semester courses in physics or related fields. These twelve courses normally include the introductory sequence (through a semester of quantum mechanics) and math through multivariable calculus and linear algebra. After that, almost everything you can think of counts either as a physics course or as a related course. So you can concentrate in physics without actually taking that many physics courses. However, if you’re sitting here figuring out how few you can get away with, you might be happier in another department. We’re serious when we say twelve semester courses in physics or related fields. These related fields’ courses might include offerings of the Chemistry, Mathematics, Applied Mathematics, Computer Science, Astronomy, Engineering, Statistics, and other departments. Check them out! 6
If you’re looking for a well-rounded physics education, the honors course requirements serve as a good guideline. (Most people do honors, especially since there’s no thesis, tutorial, or general exam requirement; most departments require at least a thesis.) For an honors degree, thirteen to fifteen courses are required, including the introductory sequence, two math courses beyond multivariable and linear algebra, and the advanced laboratory class (Physics 191r). Quantum beyond the first semester and thermodynamics/statistical mechanics courses are highly recommended, especially for those considering graduate work. If you already know single- variable calculus, you may be able to place into a higher math course and reduce the number of courses required for honors to as few as thirteen. Joint Concentrations So now that you’re taking 50 million classes, what about combining a physics concentration with something else? If you have a very strong interest in another area, you may want to consider a joint concentration (Harvard speak for a double major). Joint concentrations often require the completion of honors requirements in both departments. While this sounds like a gargantuan task, it’s usually feasible. Some fields combine quite naturally with physics. For example, “physics and math” works out to a mere three semesters of math beyond multivariable calculus and linear algebra (including one analysis, one abstract algebra, and one geometry course) among your thirteen courses for the Honors Physics degree. “Physics and Astrophysics” is also easy; just substitute the astrophysics laboratory course for the lab course offered by the Physics Department, and take five semesters of astronomy (16, 17, 98, and two others that count as related courses in Physics). If that’s all you do, you may ask why you should bother to declare a joint concentration. Perhaps most simply, it lets potential employers/graduate schools/significant others know what your real interests are. A joint concentration will also give you greater access to both departments. Some fields, on the other hand, do not combine with physics quite so naturally. For a joint concentration like Physics and Classics, you’ll really have to talk with the Head Tutor of each department. “Negotiate” might be the more appropriate term, but do not despair — with a bit of persistence all things are possible. And, such joint concentrations have probably been done before! (You will probably soon learn the story of one dedicated concentrator in Physics and Music and the physics-related musical he wrote. Another student who graduated in 2009 did a special concentration combining physics and theater; her thesis was a play on quantum mechanics!) Also, a joint concentration in physics is easier than one in many other areas. If both departments require a thesis for an honors degree, then a joint concentrator must write a thesis combining the two fields. Because physics 7
does not require a thesis for honors, only the thesis requirements of the other department apply. There are a few subtleties to joint concentrations. While the “physics and math” joint concentration does not require a thesis, the “math and physics” concentration does. “Chemistry and Physics” is also a bit different — it is a single concentration blending the two fields, technically not a joint concentration. No, it doesn’t make much sense, so read the fine print carefully! Secondary Field The Faculty of Arts and Sciences offers “Secondary Fields” at Harvard College, which may be thought of as the equivalent to what are called “minors” at other institutions. Amongst the departments offering secondary fields is the Physics Department. Students who decide not to study Physics as their primary concentration and have difficulty “negotiating” a joint concentration with another department should certainly consider this as an option! The secondary field in Physics requires 4 courses. Students must take one course in electricity and magnetism (usually Physics 15b or 153), one course in wave phenomena and/optics (normally 15c), and one course in quantum mechanics (normally 143a). The final course should simply be a physics course at the 100 level or higher. Of course, students are welcome to take courses of higher level that cover the specified material. Note that although mechanics (normally 15a or 16) is not required for a secondary field, it is a prerequisite for almost all other physics courses and is strongly recommended. More information on the details and procedures of this option can be found in the Handbook for Students online. Interested students should, as always, consult Dr. Morin or Prof. Georgi! Other Options for Physics Concentrations The Undergraduate Teaching and Education Program (UTEP) option is great if you have an interest in education; you will receive teaching certification along with your bachelor’s degree. The education requirements are quite significant, though, so for this concentration you’ll want to plan ahead. You’ll need some time for the student teaching senior year! (That may seem far away now, but it’ll arrive before you know it.) Biophysics is great if you have interests in biological questions from a physical standpoint. As a very research-oriented option, coursework is flexible enough for concentrators to continue with classes in the physical sciences, many of which have departmental courses at the intersection with biology. Work in a professor’s lab is required instead of the standard physics laboratory course. For more information on working with professors, please see the “Research At Harvard” section. 8
For the experimentally-oriented among you, there is also an Applied Physics option. It combines hands-on physics, the advanced laboratory 191r, and Engineering Sciences classes. Not Concentrating at All Maybe you’re interested in physics but you’d rather spend most of your time doing something else. Great! You can still take a lot of physics classes. As a first year, there are a few different options of introductory sequences that you can look into: 12a and 12b; and 15a (or 16 or 19), 15b, and 15c. For the life sciences, or if you are interested in medical school, be sure to look into the Physical Sciences 1, 2 and 3. You will typically need to have these classes under your belt to take a higher-level course, but all the requirements are negotiable – just talk to Prof. Georgi or Dr. Morin. In particular, we often see math, chemistry, or even computer science concentrators taking quantum mechanics (143a). Certain other classes are not as mathematical as most and are also worth thinking about. More advanced undergraduates in the sciences should be well-qualified to take many 100-level physics classes. Master’s Degree Beyond the different concentration tracks, you may also have the option of getting a master's degree concurrently with your A.B. in four years. Check the Harvard College website for eligibility requirements, as the rules have recently changed. An extremely challenging courseload is necessary to satisfy the requirements, so very few students pursue this option. When pursuing the A.M., you continue to live as an undergraduate for four years and can fulfill the requirements with classes taken at any point during your college career. The A.M. requirements typically consist of eight classes, with at least six being grad classes and at least four being physics. Chem/Phys concentrators may also want to consider the A.M. in Chemistry. Talk to upper- class students and Dr. Morin or Prof. Georgi for more information. 9
Physics Course Strategies We can't be sure that this advice will be useful to everyone, but if you learn the same way most of us do, these hints may help your physics career run more smoothly. Here are some general strategies that many of us wish we had learned sooner. • Talk to other students! Upper-class students are the most valuable source of information about anything at Harvard. They can tell you about courses, professors, research opportunities, summer programs, ways around bureaucratic obstacles, where the party’s at — in short, how to get the most out of your Harvard experience. If the people you talk to don't know the answer to your question, chances are they know someone else who does. Self-promotion time: coming to SPS events is a great way to meet older physics concentrators (and people who like physics, or people who like people who like physics). The first few SPS events focus heavily on course advising and getting to know older physics concentrators. You should also feel free to contact the SPS officers at any time; see the back cover for contact information. There is of course plenty of free advice (and addictive food) to be had at SPS events, but you should also take advantage of the other opportunities/people available to you. • Look into classes with your omnipotent friend Q If you go to the COOP a few days before classes, you should have a chance to look at the text for each class. Look at the first chapter. How do you feel? Now open the book to the middle. Excited? Great! Also, for both physics and non- physics courses, consult the Q-Guide to see how students have rated the course in the past. Note, however, that the professor for the course may have changed; the Q-Guide will point you to another course they have taught if possible. Take this information into account! The professor makes the course!!! Check the online Q-Guide for ratings from previous years: www.fas.harvard.edu/~evals. • Take advantage of shopping period The surest way to assess a course and its professor is to attend the lectures during shopping period. Be sure to grab a syllabus. This is your chance to check out all the courses you're considering — and you should look at more courses than you plan to take. Even if you think you already know what you're taking, shop around. You may discover a wonderful class you never even knew about, or you can get a glimpse of courses you may take in the future. Science classes generally dive right into material, so be prepared to take notes and have a way to copy them once you finalize your course selections. Don’t take a class you don’t enjoy in the first few lectures. Studies have shown that 10
initial impressions of Harvard classes are almost always correct. • Get the best section leader In most physics courses you won't be required to attend section, but we feel that a good section can greatly enhance your experience. If you are dissatisfied with your assigned section, don't just stay home; find the section most worthwhile for you. If you're required to attend a particular section with which you are unhappy, keep in mind that a “schedule conflict” could make a section change necessary. Just because a section is optional doesn't mean it's useless — attending section helps reinforce the material you're learning, demonstrates how to work college-level problems, and gives you an opportunity to ask questions about points that confuse you. Plus, a TF who sees you regularly in section may be friendlier when you come to ask her for help on your problem set. It’s also good to get to know grad students: they can be very cool people, and they will also expose you to the kind of life that you might live for the next 5-10 years, should you continue in physics. They can also introduce you to their own research and their professors and tell you where to find free food. • Go to your professors' office hours! Remember when you were thinking about going to Harvard and everyone warned you that you would never have any contact with professors? This is your big chance to prove them wrong! You can use professors' office hours to get help with difficult course material, find out about their research, or discover that they have lives outside physics. You will have to go out of your way to seriously interact with most professors, but most will be delighted to see you at their office hours — don't be intimidated! Several lonely professors have been overheard begging students to visit their office hours. • Use the Undergraduate Physics Study and the Physics Reading Room The Undergraduate Physics Study (Jefferson 251) is an area specifically reserved for undergraduates to work, relax, and chat with friends. The study is right next to the offices of Dr. Morin, the Co-Head Tutor, and Carol Davis, the Undergraduate Coordinator. Look for SPS events, TF office hours, and free food here! Located on the fourth floor of Jefferson Laboratory, the Physics Reading Room (formerly Physics Research Library) is one of the most pleasant places to work or relax on campus. The library is open to all Monday-Friday 9AM-5PM, but anyone with keycard access to Jefferson (including all physics concentrators) has 24-hour access. This space is open to the entire physics community, whether you want to do research, work on a problem set, or read the newspaper. And don’t forget the cookies every Monday afternoon before the departmental colloquia – they can be found here. 11
• Work with other people on problem sets! We cannot emphasize enough the importance of this. On a practical level, a study group will make your life easier on problem set night and help you understand the material more fully. More importantly, you’ll meet and get to know your fellow concentrators. If you’re taking a class aimed at physics concentrators, check out the Eliot dining hall on Wednesday nights – it is where many students, especially those in the intro classes, do their problem sets, in a celebrated weekly tradition known as Physics Night (the same goes for Math Night on Monday nights). There are always substantial supplies of baked goods available to fuel this endeavor. Eliot is usually chock-full of physics concentrators until the wee hours of the morning. Nights at Eliot usually end up being one of the best parts of being a physics concentrator at Harvard. If you’re going to work outside Eliot, assembling a study group might take some persistence. But don't be shy about asking people to work with you. If you can’t find a study group, just email sps-open. Also try Facebooking people in your classes (no it’s not sketchy, and yes, it really works), or come to SPS meetings to meet other people in your classes. We feel obligated to warn you: don't rely on your study group as a crutch — copying answers for problem sets won't help on the exam. And it is technically academic dishonesty and could get you in trouble. We hope that you’ll find that your fellow students are more valuable as teachers than as sources of answers. • Check out previous final exams. Final exams for many courses are available at Gordon McKay Library of Engineering and Applied Sciences and the Harvard University Archives. Recent exams are often posted on course webpages. Studying problems from old exams is a great way to prepare for your own final. Beware, however, if the professor for the class has changed, because the final may be entirely different. 12
Course Descriptions and Recommendations We are only providing brief course descriptions here since you can look up more detailed descriptions in the my.harvard portal. However, we’ve also offered some opinions that you won’t find in the official descriptions. Just remember that these are our opinions; yours may differ. Also, the prerequisites listed in the course guide are not always up-to-date. Check with the professor if you are considering not following them, however. The prerequisites listed below are also our opinions. Due to editorial constraints (i.e. the Physics Department gives us money) we are unable to rate professors as well as courses. You should be aware, however, that in many cases the satisfaction one gains from a class has more to do with the professor who is teaching it than the course material itself. The Q-Guide is an excellent resource for professor ratings. If you wish to find professor ratings from previous years, back issues of the Q-Guide can be found at www.fas.harvard.edu/~evals. Students who have taken the course provide an even better source of information. (Always feel free to badger your SPS buddy or the SPS officers about such things; we’ve certainly done our share of asking for info!) We can’t emphasize this strongly enough: Ask around about professors and courses!! Also, the professors themselves are good source of information. You might want to talk to them, to watch them in action during shopping period, or both. We suggest that if you are unsure of which course is right for you, talk with the professor giving the course. If you think you may be familiar with the material in a course, check out the past course webpages and final exams. Take a look at these to get an idea of the level of the course. Even better, find out when this year’s professor last gave the course, and check the final exams from that year, available at Gordon McKay Library of Engineering and Applied Sciences. Below we have included all undergraduate courses offered by the Physics Department, and many courses in the related fields. Courses in brackets are not offered this year. NOTE: Courses demarcated with [brackets] will not be offered this year. Those marked by an asterisk (*) are courses you should especially consider during your first year. The rest you might just want to mull over for a while. (Or, as Nobel Laureate Leon Lederman said: “Put your nose to the glass and look at all the candy!”) 13
Freshman Seminars Freshman seminars are very different from most other courses you will take in your first year. In these courses, a small group of students works closely with a professor in the investigation of a field—there is a great deal of informal interaction in addition to standard classroom fare. A freshman seminar can supplement the introductory sequence (see below) if you think you may concentrate in physics; it can also be a great way of dabbling in physics if you’re sure you won’t concentrate in it. The only good reason not to take a seminar is time. These courses are electives. If it’s important to you to get started on the introductory sequences in physics, math, and chemistry all at once, then you might not have time for a freshman seminar. Still, don’t discount the option without some thought; a freshman seminar (inside or outside your field) can be one of your best academic experiences at Harvard. We heartily recommend considering a freshman seminar in any area that piques your interest; here we list those related to physics. Also consider taking a freshman seminar not in physics – it’s a great way to expand your interests. Note that there are many seminars not listed here related to the other sciences as well. * Freshman Seminar 21G (Loeb): First Stars and Life in the Cosmos (Spring) * Freshman Seminar 21V (Strominger): Black Holes, String Theory, and the Fundamental Laws of Nature (Fall) * Freshman Seminar 22I (Bloxham): The Science of Sailing (Fall) * Freshman Seminar 23C (Woodin): Exploring the Infinite (Fall) * Freshman Seminar 23P (Vafa): Physics, Math and Puzzles (Fall) This seminar is intensely rewarding for students interested in physics, mathematics, and the interface between the two. Simple yet profound results in physics are explored through the unique medium of puzzle-solving. Consider this puzzle: There are four cities at the corners of a square. You have to build roads so that you can drive from any city to any another in some way. How do you do it using the minimum length of road? The answer has to do with why particles have mass. The ideas explored in this class, including symmetries and duality relations, will come up over and over in future physics classes. The light workload of an interesting puzzle to think about each week makes the class an ideal addition for a busy schedule. * Freshman Seminar 23R (Alcock): Asteroids and Comets (Spring) * Freshman Seminar 23Y (Doyle): All Physics in 13 Days (Fall) 14
* Freshman Seminar 26J (Randall): The Universe’s Hidden Dimensions (Fall) * Freshman Seminar 51C (Meade): Science in the Age of Artificial Intelligence (Fall) * Freshman Seminar 51H (Zipser): Models of the World: Explaining the Past and Predicting the Future (Fall) * Freshman Seminar 51T (Dvorkin): The Universe: Its Origin, Evolution, and Major Puzzles (Spring) * Freshman Seminar 51U (Georgi): Insurrection in a Little Kingdom—The Real Story of the Standard Model of Particle Physics (Spring) * Freshman Seminar 51V (Kim): Physics of Measurements: Experimental Science (Fall) * Freshman Seminar 51X (Samuel): Changing Perspectives: the Science of Optics in the Visual Arts (Spring) * Freshman Seminar 51Z (Finkbeiner): The Path to a Low-Carbon Future (Fall) * Freshman Seminar 52D (Vishwanath): Quantum Entanglement and the Second Quantum Revolution (Fall) * Freshman Seminar 52E (Park): Science and Technology Primer for Future Leaders (Spring) * Freshman Seminar 52H (Franklin): The Interaction of Light with the World (Spring) Seminars require an application and, occasionally, an interview, but are well worth the effort. More information and a complete listing of seminars are available here: https://freshmanseminars.college.harvard.edu/seminars. 15
Physics Department Courses Introductory Courses Physical Science Courses: * Physical Sciences 1, 2, 3: an introduction to the physical sciences for biological applications (1,3 Spring; 2 Fall) These are the introductory courses to physics as well as physical chemistry with an emphasis on biological applications. They are intended especially for pre-med students, but are recommended for any students who are interested in the physical sciences but do not have much background (though AP Chem is helpful). Among other things, Physical Sciences 1 (PS1) covers introductory general and physical chemistry, while PS2 and PS3 cover mechanics and electromagnetism, respectively. Note that PS2 and PS3 are not accepted for credit towards a physics concentration, though they are accepted for other concentrations, such as chemistry. Students should consult the department for more information. * Physical Sciences 10: Chemistry: A Microscopic Perspective on Molecules, Materials, and Life (Fall) * Physical Sciences 11: Foundations and Frontiers of Modern Chemistry: A Molecular and Global Perspective (Spring) These courses, besides your typical introductory general chemistry material, intend to introduce fields and applications that you might not get to outside of more advanced physics and chemistry classes. PS 10, for instance, goes over the fundamentals of quantum mechanics and statistical mechanics, while PS 11 looks at topics such as thermodynamics and quantum chemistry (overlapping topics with PS 1 as well). Both emphasize real-world applications, such as medical imaging, global warming, and electric cars. These courses can also be taken independently of each other. Pre-med general chemistry requirements can be fulfilled with any two courses from Life and Physical Sciences A, Life Sciences 1a, PS 1, PS 10, and PS 11. Students should consult the department for more information. * Physical Sciences 12a,b: Mechanics (Spring) and Electromagnetism and Statistical Physics (Fall) from an Analytic, Numerical, and Experimental Perspective These courses comprise a standard college-level one-year introduction to physics, with emphasis on engineering applications and experimental data analysis. They satisfy medical school requirements and are highly recommended for a pre-med concentrating in an area other than physics but looking for a more rigorous treatment than PS2 and PS3. PS 12a,b is accepted for credit in many concentrations, including chemistry and engineering. Math 16
21a is listed as a corequisite; however, if you are comfortable with your calculus skills it may not be necessary. If you wish to count PS 12a,b toward the Physics or Chem/Phys concentrations, be sure to consult the department to develop a coherent plan of study. * Applied Physics 50a,b: Physics as a Foundation for Science and Engineering These courses form a unique year-long project-based introduction to physics. They are relatively new, and promise to provide the equivalent of a standard introductory physics course, but with a heavy emphasis on engineering- inspired group projects. Math at the level of Math 1b concurrently is required, though it’s recommended to take Math or Applied Math 21a concurrently; math content will be coordinated with AM 21a. Consult the department for more information. Note: Where Math 21a is listed as a pre/corequisite, Applied Math 21a or Math 23b, 25a, or 55a will also satisfy the requirement. Similarly, Applied Math 21b or Math 23a, 25b, or 55b can substitute for 21b. Physics Courses: * Physics 15a: Introductory Mechanics and Relativity (Fall and Spring) * Physics 16: Mechanics and Special Relativity (Fall) [* Physics 19 (formerly Phys 101): Introduction to Theoretical Physics] Ah, the great first-year dilemma. Physics 15a, 16, and 19 are your choices for your first physics class as a physics concentrator – you can take any one of the three; they all feed into the same sequence (15a/16/19, 15b, 15c, 143a). Basically, 15a and 19 are hard, while 16 is very hard. They all go beyond the high school AP Physics level and introduce all sorts of interesting topics. Many freshmen are not sure whether they will be able to handle 16. Fortunately, the Department makes it easy to switch between courses at the beginning of the semester once you get a feel for them. You probably want to take a look at 16, but don’t feel obligated to take it. Depending on what you took in high school, it might be a better idea to hone your math background first – 16 is very demanding mathematically. And if you’re planning on taking other difficult classes, there’s no point in killing yourself with work. On the other hand, Physics 16 is a trial-by-fire bonding experience for those who take it. Many who take it call it one of the standout experiences of their Harvard career. Phys 19 covers a wider set of foundational topics in slightly less depth for theoretical physics than 15a and 16, and is intended to give a broader preview of later courses in the physics concentration. Phys 19 is a designed to accommodate a wide range of backgrounds and interests: it assumes only a familiarity with single-variable calculus, and teaches the necessary mathematical background along the way. Since the course structure consists of 17
problem sets and a final project, there are plenty of opportunities for those that wish to engage deeply with the material to further enrich their understanding; for those that are just interested in a taste of a bit of everything, Phys 19 has a place for you too. The main point of 15a and 16 is to learn mechanics and solve challenging problems simply because physics is cool. The main point of Phys 19 is to provide a comprehensive grounding and experience in the concepts and mathematical tools of theoretical physics that show up in the rest of the physics concentration. But also because physics is cool. For 15a, concurrent enrollment in Math 1b is required (with 21a highly recommended), while for 16 concurrent enrollment in Math 21a or an equivalent is required: most students in 16 last year took one of Math 23/25/55. And by the way, we also recommend 15a for non-concentrators who wish to take physics and come out with a fairly deep understanding of mechanics (many chemistry and engineering concentrators choose this option). * Physics 15b: Introductory Electromagnetism (Fall and Spring) Physics 15b covers electricity and magnetism at a level significantly beyond AP, and follows 15a/16/19 in the introductory sequence. Non-concentrators will often take the class, leading to a wide range in students’ experience. However, the course is flexible and provides plenty of support or challenge no matter what your physics background. Math 21a is a formal corequisite; however, we recommend a multivariable background coming into the course. A few students each year consider skipping 15b to take 153 (Electrodynamics). Consult with Prof. Georgi and think long and deeply before deciding. Remember that the PSI lab for 15b is still required of all concentrators. Physics 15c: Wave Phenomena (Fall and Spring) This is a course in waves and optics. It covers important material for future courses, including the wave equation, Fourier analysis, and a formal introduction to oscillations. Oscillations are the basis of quantum mechanics, and 15c will provide powerful tools for future physics courses (even if balls on springs and pendula seem boring to you now). Math 21b is a corequisite. Most of those taking this course are physics (or astronomy) concentrators, though some chemists interested in physical chemistry take it as well. There are also still plenty of people there for interest’s sake, and we encourage non- concentrators who have the time to get at least this far. Note that this course, more so than 15a and 15b, can be a noticeably different experience under different professors who may take different approaches or cover different topics. Ask around and check the Q Guide for opinions. If you 18
are considering taking Physics 175 or another course to fulfill the 15c requirement, consult with Prof. Georgi and think carefully before making this decision. Remember, the PSI lab for 15c is still required for all concentrators. Physics 143a: Quantum Mechanics I (Fall and Spring) Ah, quantum mechanics. As Prof. John Doyle puts it, “this class is what separates physicists from everyone else.” This course is required of all concentrators and is a prerequisite for most of the cool upper-level physics courses. Physics 15c is a prerequisite (although every year a few students with a strong background skip 15c). Math 21b is also a definite prerequisite; we feel that the more linear algebra you know, the better you will understand the material. (Math 23a, 25a, or 121 will make this course even more worthwhile!) If, by the time you are ready to take 15c, you are already strong in linear algebra, Fourier Analysis, and understand the wave equation, you may consider taking 143a concurrently with 15c, but having previously taken 15c makes 143a much, much more comprehensible. Taking 151 (Mechanics) before this class also helps, especially with Hamiltonians, although not many concentrators go that route, and Hamiltonians aren’t difficult to pick up during 143a. Concentrators in other sciences often take this course, especially chemists as an alternative to the quantum course in the chemistry department. The course will have a very different flavor from Chem 160, so consider this decision carefully. The above introductory physics courses are offered every semester (except Physics 16 and 19, which are only offered in the fall), so if you think that you don’t want to start right in (though we can’t imagine why you wouldn’t) but later have a change of heart, you don’t need to spend a whole semester twiddling your thumbs and waiting for the intro course you want to take. If you do take your physics classes “out of phase,” they will be smaller and may have a different set of professors. But once you finish 143a, you’ll be back in sync with the rest of the concentrators. Courses Beyond the Introductory Sequence Physics 125: Widely Applied Physics (Spring) This course uses physics to analyze important technologies and real world systems; it emphasizes physical intuition and order-of-magnitude calculations. It aims to develop a toolbox that all physicists should have at their fingertips. The 15a/b/c series is a prerequisite, with 143a recommended at least as a concurrent course. The material covered in this course varies greatly depending on the instructor. Physics 129: Energy Science (Spring) Consult the department for more information. 19
Physics 141: The Physics of Sensory Systems in Biology (Fall) Consult the department for more information. Physics 143b: Quantum Mechanics II (Fall) This course takes what you learned in 143a and uses it to study all kinds of physical systems. The exact details of what is covered vary from year to year, but they generally involve atomic systems and approximations. You won’t learn much more about fundamental quantum theory in 143b; the main developments are different ways to approximate various situations to make them amenable to solution by quantum mechanical means. However, keep in mind that 143b covers some basic material physicists are expected to know and that you might not get in any other class; atomic and molecular physics are fundamental applications of quantum mechanics. Physics 143b will not only firm up what you learned in 143a, but it also opens the doors to many modern fields of research, like condensed matter physics, quantum information, and AMO theory. It may be a little tedious for some, but you’ll be a better physicist for it – and it’s critical for grad school. For all the Chem/Phys students out there, keep in mind that this is the class in which you’ll learn why elements, atoms, and molecules work the way they do. And often the last week is an introduction to quantum computing. Interested? Awesome! Physics 145: Elementary Particle Physics (Fall) Elementary particle physics is a large and difficult area that requires a great deal of mathematical and physical preparation to understand fully. Most students never see much of the theory until graduate school. This course successfully remedies that situation by focusing on intuitive understanding of the concepts involved rather than the calculational aspects. This is usually a small class, with a greater opportunity for interaction with the professor both in and out of the classroom. A fun and rewarding course that is highly recommended! Physics 151: Mechanics (Fall) This course studies mechanics from a more advanced point of view than 15a or 16, starting with the Lagrangian formulation. However, once you get past Lagrange’s and Hamilton’s equations, there is a lot of time left over, and the course seems to vary greatly with the idiosyncrasies of its instructors. Because of this, we suggest that you do some research before taking this course, to find out what the instructor plans to cover. Many concentrators choose to skip this class because the math can get dense, but classical mechanics can be pretty interesting. Taking this course concurrently with 15c is a great way to prepare for 143a, which will involve lots and lots of Hamiltonians. Oftentimes, this course covers topics like classical field theory and forays into the connection 20
between classical and quantum mechanics via discussions of the Feynman path integral. These topics are especially important for budding theorists! Physics 153: Electrodynamics (Spring) Physics 153 is an intermediate course in electrodynamics. It reconsiders the non-electronics material of 15b with greater mathematical sophistication and overall depth. Prior understanding of concepts from electricity and magnetism are assumed, however, so we do not normally recommend skipping 15b to take 153 (certain topics, such as circuits, are not covered in 153; hence the asterisk on the asterisk). Some professors also spend part of the course covering important mathematical techniques (e.g. Bessel functions). Some students are particularly happy with David Griffiths' Introductory Electrodynamics, which is typically the text for this course. [Physics 160: Introduction to Quantum Information] Physics 160 is a wonderful and wide-ranging introduction to the nascent but booming field of quantum information, guided by one of its foremost torchbearers, Prof. Misha Lukin. The course starts with a basic review of quantum mechanics, the concept of two-level systems, and an introduction to open-quantum systems and entanglement, and ends by describing the state of the art in quantum algorithms and the research frontier in quantum simulation (including many experiments in the Harvard-MIT region). All along, the class strives to build up strong intuition in quantum information, and at the end of the semester leaves students with enough background to genuinely begin research in the field (this is not an exaggeration). If you’re interested in quantum computation and quantum information, this is the class for you. Even if you think that quantum computing is malarkey, take this class to get more in depth practice with topics from quantum mechanics such as density matrices, two level systems, entanglement, and dynamics. Such topics, usually covered rapidly in 143a and 143b, are integral to many research areas (condensed matter, atomic physics, and of course, quantum information), and developing intuition for them is often essential. Physics 175: Laser Physics and Modern Optical Physics (Spring) Introduction to quantum electronics (laser physics) and modern optical physics aimed at advanced undergraduates, with an emphasis on applications. This course is often taught by Marcus Greiner who brings a superlative experimental perspective (and sweet demos too) to the course. Physics 181: Statistical Mechanics and Thermodynamics (Spring) For perhaps the first time in physics, you’ll be looking at not one-body, not two-body, but 1023-body systems! This course, or Engineering Sciences 181 or Chemistry 161, is strongly recommended for concentrators at some point. You really can’t get by as a physicist without knowing something about this stuff. 21
The Physics Department course is more geared towards statistical mechanics, while the ES course emphasizes thermodynamics. Chemistry 161 covers much of the same material, but with a focus on applications to chemistry. Physics 143a is a prerequisite. Physics 195: Introduction to Solid State Physics (Fall) Get ready to apply your newly gained quantum and statistical mechanics skills to a very important system: Solids! Starting with the classical Drude theory of metals, the course aims to derive the electronic and thermal properties of metals, insulators and semiconductors by applying quantum mechanics to periodic systems. It is an essential course for research in condensed matter physics! This course is typically jointly offered as Applied Physics 195. Applied Physics 195: Introduction to Solid State Physics (Fall) The same class as Physics 195, but jointly listed through SEAS. Laboratory Courses * Physics 123: Laboratory Electronics (Fall and Spring) This course in laboratory electronics presents the skills needed to construct scientific instruments, a valuable ability for those wanting to go into experimental physics or just those wanting to leave Harvard actually being able to do something useful. The broad introduction to analog and digital electronics is also valuable for engineering concentrators and some Computer Science concentrators; both undergrads and grad students take the class. There are no formal prerequisites, but at least high school physics and some familiarity with calculus is useful. Previous experience with basic electronics or low-level programming can be immensely useful. Engineering Sciences 151, 154 and 156 cover similar topics, but the physics course is more focused on “seat-of-the-pants” electronic design emphasizing broad understanding over calculational proficiency. As might be expected, the class requires a substantial time commitment, but you get out of it everything you put in. Estimates of workload range from 1.5 to 2.5 normal classes. [Physics 191: Advanced Laboratory] In this laboratory course, required of all honors concentrators (and highly recommended for all concentrators), students carry out three experiments chosen from a list. These are not your basic high school measure-g-with-a- pendulum-and-stopwatch experiments: topics include superfluid helium, the lifetime of the m-meson, and Nuclear Magnetic Resonance. Physics 15abc is required, and 143a is highly recommended. The actual knowledge needed for these courses is highly dependent on the experiments performed; some experiments make more sense if you’ve also taken 181. If you are leaning towards Astrophysics (and have taken enough courses in that department), talk to the head tutors about the possibility of taking Astronomy 191 instead. 22
The 90's: Research, Reading, and Ice Cream Physics 90r/91r: Supervised Research/Reading (Fall and Spring) These two courses allow students to pursue research or reading in areas of physics not covered in the curriculum or in which more in-depth knowledge is wanted. They are very valuable for those who think they may wish to pursue physics after their undergraduate years. Since the subject matter can be anything, so can the prerequisites. See the section on research for hints on figuring out what to study. These courses sometimes culminate in a senior thesis. Do not hesitate to reach out to professors to discuss the possibility of pursuing supervised reading or research! Many students find this experience incredibly helpful. Physics 95: Topics in Current Research (Fall) Physics 95 is first and foremost a course in science communication, with an emphasis on upperclass-level physics. The centerpiece of the class is the three 20-minute oral presentations that each student is required to give throughout the semester; individual attention is given by the professor in this seminar- style course to every student's presenting skills, ensuring that you walk away with a clear understanding of how to get in front of people and give an engaging, comprehensible talk about any subject. Directed toward juniors and seniors, this course offers a wider variety of topics to titillate the imagination. The course is complemented by weekly Wednesday evening lectures by different Harvard professors; each professor discusses their ongoing research, and free post-lecture ice cream is served every week. (These evening lectures are open to all physics students, not just the enrollees in Phys 95!) This course is an excellent opportunity to learn about the ongoing research interests of the faculty, to develop effective communication skills as a scientist, and to follow up on one research topic from lecture in the required term paper. 23
Graduate Courses Some undergraduates in the past, usually after completing the corresponding 100-level course, have ventured on into the realm of graduate courses. These are often very different from undergraduate courses due to the differing needs of their students, and typically they represent quite a significant workload. That disclaimer aside, here are a few graduate courses highly advanced undergraduates have taken with success. Physics 210: General Theory of Relativity (Spring) General relativity is the final course a student takes in classical theory. Curved spacetime, black holes, an expanding universe, the whole nine yards. Physics 210 is not a prerequisite for many other courses aside from Physics 211r; it is an end in itself. The mathematical tools required, such as familiarity with tensors and differential geometry, are developed naturally as the course progresses. However, it may take a while to get to the actual physics of the class. Long, tedious calculations of quantities involving rank-4 tensors are a staple of the coursework - so be prepared. All the effort is worth it in the end, as the course provides a great introduction to general relativity. [Physics 216: Mathematics of Modern Physics] This course requires significant prior background in mathematical physics, and it assumes knowledge of a lot of mathematics from real and functional analysis to quantum field theory. As an advanced survey covering particular topics in great depth, however, it is an excellent course. Physics 232: Advanced Classical Electromagnetism (Spring) This course definitely requires some sort of previous background in electromagnetism, ideally at the advanced undergraduate level of Physics 153. The syllabus begins with relativity and quantum mechanics and explains the fundamental underpinnings of Maxwell’s Equations before going through a more traditional EM curriculum, often from J.D. Jackson’s classic textbook, to end up anywhere from magnetic monopoles to non-abelian gauge theories to superconductivity. This is a great course for learning about electromagnetism in depth. Be aware, though, that the material covered in the latter parts of the course may vary greatly depending on the professor. Physics 251a/b: Advanced Quantum Mechanics I/II (a Fall, b Spring) As the introductory quantum sequence for graduate students, Physics 251a/b offer an advanced, fresh beginning for quantum mechanics. Starting from scratch, the class clarifies the mathematical and physical foundations of quantum theory. Instructors vary in pace and material, but typically the class moves quickly and the lectures are at a high level. Students who have completed the 143a/b sequence and are interested in strengthening their quantum mechanics foundations should keep these classes on their radar. 24
Physics 253a: Quantum Field Theory I (Fall) Physics 253a is the first course in the graduate quantum field theory sequence. You will want to take a quantum field theory course at some point in your career if you are interested in high-energy physics, nuclear physics, or condensed matter physics, and it is nice to have some understanding of the subject if you intend to continue your studies in physics at the graduate level. While it is a very advanced course, you can probably handle it if you have taken at least Physics 143a and 143b. Physics 151 might also be helpful to gain a grounding in classical field theory, but it is not strictly necessary as the course typically starts with a fast-paced introduction. The course is often taught by Prof. Matthew Schwartz, whose celebrated textbook Quantum Field Theory and the Standard Model provides a good introduction to the subject and is usually the text of choice for the class. The problem sets will require a very significant time commitment, however, and you should bear in mind that Physics 253a is not a great addition to an already crowded schedule. Quantum Field Theory is an incredibly vast subject, so while this course offers a very solid introduction to the field (Chapters 1-19 of Prof. Schwartz’s textbook), keep in mind that there is much more to come. Also note that while MIT has a 3-semester QFT series just like Harvard, Harvard’s version covers significantly more material in a shorter amount of time. Physics 253b: Quantum Field Theory II (Spring) The second of Harvard’s 3-semester QFT series, this course starts where Physics 253a leaves off and turns the difficulty up tenfold. It covers the remaining chapters of Prof. Schwartz’s textbook as well as a large chunk of Weinberg’s second volume. Taking this course on its own will have you working harder than most of your peers, so only consider it if you are sure you want to do high energy or condensed matter theory. You may also want to consider Physics 254 when it’s offered as a good, less extreme alternative. Physics 253c: Quantum Field Theory III (Fall) The third of Harvard’s 3-semester QFT series, this is a topics course which covers different material based on when it is being taught. This course is a very exciting gem once you’ve taken Physics 253a, and may cover topics such as supersymmetry or conformal field theory. Physics 254: The Standard Model (Spring) An amazing sequel to Physics 253a, this course puts the material you learned in Physics 253a to good use by introducing the building blocks of the Standard Model. If you ever wanted to go beyond the Quantum Electrodynamics from Physics 253a, and learn about the weak and strong forces, as well as the Higgs Mechanism, this is the course you’re looking for. While you can take it along with Physics 253b, students usually take one or the other. 25
You can also read